Space of modular forms of level 24, weight 6, and trivial character

• Label: 24.6.a
• Level: $24$
• Weight: $6$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $24$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(24\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(24))\).

	Total	New	Old
Modular forms	24	3	21
Cusp forms	16	3	13
Eisenstein series	8	0	8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(5\)	\(1\)	\(4\)		\(3\)	\(1\)	\(2\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(6\)	\(1\)	\(5\)		\(4\)	\(1\)	\(3\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(7\)	\(1\)	\(6\)		\(5\)	\(1\)	\(4\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(6\)	\(0\)	\(6\)		\(4\)	\(0\)	\(4\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(11\)	\(1\)	\(10\)		\(7\)	\(1\)	\(6\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(13\)	\(2\)	\(11\)		\(9\)	\(2\)	\(7\)		\(4\)	\(0\)	\(4\)

Trace form

3 * q - 9 * q^3 + 98 * q^5 + 24 * q^7 + 243 * q^9 + 20 * q^11 - 102 * q^13 - 198 * q^15 - 266 * q^17 - 5364 * q^19 + 1944 * q^21 + 4904 * q^23 + 2061 * q^25 - 729 * q^27 - 10422 * q^29 + 1920 * q^31 + 9252 * q^33 + 26256 * q^35 - 1662 * q^37 - 16398 * q^39 - 23202 * q^41 - 13068 * q^43 + 7938 * q^45 + 3216 * q^47 + 42315 * q^49 - 22050 * q^51 - 64846 * q^53 - 11592 * q^55 + 7164 * q^57 + 51236 * q^59 + 37098 * q^61 + 1944 * q^63 + 38396 * q^65 - 11364 * q^67 + 1800 * q^69 - 32264 * q^71 + 24510 * q^73 - 48807 * q^75 + 37920 * q^77 + 39120 * q^79 + 19683 * q^81 - 57524 * q^83 - 199068 * q^85 + 165186 * q^87 + 32046 * q^89 - 9264 * q^91 - 71136 * q^93 - 130040 * q^95 - 180954 * q^97 + 1620 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
24.6.a.a	$24$	$6$	24.a	1.a	$1$	$1$	$1$	$3.849$	\(\Q\)	None	✓	✓	✓	✓	24.6.a.a	$1$	$1$	\(0\)	\(-9\)	\(-34\)	\(-240\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-34q^{5}-240q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.b	$24$	$6$	24.a	1.a	$1$	$1$	$1$	$3.849$	\(\Q\)	None	✓	✓	✓	✓	24.6.a.b	$1$	$0$	\(0\)	\(-9\)	\(94\)	\(144\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}+94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.c	$24$	$6$	24.a	1.a	$1$	$1$	$1$	$3.849$	\(\Q\)	None	✓	✓	✓	✓	24.6.a.c	$1$	$0$	\(0\)	\(9\)	\(38\)	\(120\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+38q^{5}+120q^{7}+3^{4}q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(24)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)